For the exterior, a painted wooden door is a tough surface to protect. Acrylic finishes will usually outperform oil-based paint on a wooden door due to their breathability and flexibility. While oil-based finishes offer superior flow and leveling during application, oil- based coatings generally chalk, crack, and fade rapidly. If the door is already coated with an oil based product, it is usually best to sand the door, clean, prime, and apply a finish of 100% Acrylic Paint if the door gets a lot of sun.
Acrylics exhibit good color and gloss retention, and offer the flexibility needed for exterior wood. The disadvantage of the acrylics is that they dry quickly, making a slick smooth finish more difficult. You need to use flow additives, the right premium Acrylic Paint , and good technique. Try to paint in cooler temperatures, and protect the door from direct sun during application and curing.
Be careful on wooden doors covered by an unvented storm door. Trapped heat can cause some coatings to bubble, especially dark colors.